modeling of hydrogen desorption from tungsten surface...simulations and accelerated molecular...
TRANSCRIPT
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J. Guterl1, R.D. Smirnov1, S.I. Krasheninnikov1, B. Uberuaga2, A.F. Voter2, D. Perez2
1. University of California San Diego, La Jolla, CA 92093, USA
2. Los Alamos National Laboratory, Los Alamos, NM 8754, USA
2014 Joint ICTP-IAEA Conference on Models and Data for Plasma-Material Interaction in Fusion Devices
Contact: [email protected]
Modeling of hydrogen desorption from
tungsten surface
This work is performed under the auspices of USDOE Grant No. DE-FG02-04ER54739
and the PSI Science Center Grant DE-SC0001999 at UCSD 1
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Hydrogen retention and recycling on metallic plasma-facing components are among key-issues
for future fusion devices due to safety and operational reasons. For tungsten, which has been
chosen as divertor material in ITER, desorption parameters experimentally measured for
fusion-related conditions show a large discrepancy. In this paper, we investigate hydrogen
recombination and desorption on tungsten surfaces by performing molecular dynamics
simulations and accelerated molecular dynamics simulations to analyze adsorption states,
diffusion, hydrogen recombination into molecules and desorption from tungsten surfaces,
and clustering of hydrogen on tungsten surfaces. The validity of tungsten hydrogen
interatomic potential is discussed in the light of MD simulations results, and hydrogen surface
diffusion properties and effects of clustering on hydrogen desorption are analyzed. A kinetic
model is introduced to describe the competition between surface diffusion, clustering and
recombination, and different desorption regimes are identified. Characteristics of these regimes
are compared to thermodesorption experiments data.
Topics: H retention in W, H desorption from W surface, H clustering & diffusion on W
surface, Temperature Accelerated molecular Dynamics, Molecular Dynamics
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Abstract
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In future fusion devices, retention and recycling of hydrogen isotopes in PFCs
material induced by exposure of plasma facing components (PFCs) to continuous
large plasma flux (~1020 β 1024πβ2π β1 ) during long periods ( ~400π ) are among key-issues due to:
safety issues (total quantity of π»3 < 700π in ITER)
synergetic effects between plasma and PFCs
impurities release in plasma
Divertor in ITER + PFCs in DEMO are planned to be in tungsten
Retention in PFCs modeled with reaction-diffusion equations (R-D) due to large
time and space scales relevant for fusion reactor conditions
Boundary conditions of R-D equations determined by surface processes:
H desorption flux Ξπππ from W surface usually described as desorption of π»2 formed by recombination of adsorbed H atoms on surface (second-order kinetic
process):
Ξπππ = πΎ0πβπΈπππ π
πΎπ
ππ 2 (1)
Introduction 1/3
Understanding mechanisms involved in hydrogen retention and outgassing in
W is essential
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Experimental data show:
Large discrepancies for πΎ0 and πΈπππ and contradictory temperature dependencies of πΎπ (a)
Several binding states for adsorbed hydrogen on tungsten
surfaces observed in thermodesorption experiments
[Tamm1971,Markelj2013]
Desorption kinetic order may be different from 2 [Tamm1971]
Desorption parameters ( πΈπππ , πΎ0) vary significantly when hydrogen surface coverage exceeds 0.5 (b,c) [Alnot1989]
Introduction 2/3
From [Roth2011]
πΎπ
(a)
(b) From [Alnot1989]
π π’πππππ πππ£πππππ π (x10)
(c)
From [Alnot1989]
π π’πππππ πππ£πππππ π (x10)
surface processes are complex and may be not well described by (1)
+ desorption regime depends on surface coverage
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However, surface processes may not affect retention if recombination rate
coefficient is large enough (πΎπ > 10β24π4π β1) [Roth2011, Causey2002]:
True at high temperature but surface desorption regimes may be different for
thermodesorption experiments (TDE) and for divertor in ITER conditions:
In high-recycling regime: Ξππ β Ξπππ and Ξπππ < Ξπππ₯ = πΎ0 πβπΈπππ π (ππ
π ππ‘)2, ππ π ππ‘ β 1019πβ2
Better description of hydrogen desorption mechanisms from W surface is needed
We propose to investigate atomic processes governing H surface
desorption from W using molecular dynamics simulations (MD) 5
Introduction 3/3
Surface saturation by hydrogen?!?
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W W
πΈπ [ππ]
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Frozen W surface not relevant for H adsorption
W-H adsorption energy πΈπππ = πΈππ» β πΈπ» β πΈπ mapped by slowly approaching H along z-direction toward W
surface maintained at T~0K by viscous force
Hydrogen adsorption and diffusion on W surface 1/3
(T)
MD simulations setup: W-H Tersoff type potential Ξπ‘~0.1ππ Box β 8x8 lattice cells and surfaces Frozen W bottom layers
: initial position of W atoms on relaxed surface
πΈπππ >πΈπ»22
in agreement with π»2 dissociation on W surface [Hickmott1960]
Single H desorption at T>1600K with πΈπππ = 2.91ππ [Hickmott1960] surface: tight-binding potential shows πΈπππ = β2.4ππ for (B) site [Forni1992] W-H Juslinβs potential gives reasonable description of adsorption sites
(B)
(O)
(D) (T)
(B)
(O)
πΈπππ = 2.4ππ π΅ , 2.3ππ π , 2.1ππ π , 2ππ (π·) πΈπππ = 1.6ππ π΅ , 2.35ππ π , 2.4ππ π
x
y
z
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Activation energies πΈ(π)β(π) of hydrogen transition between adsorption sites needed
to characterize diffusion of hydrogen on W surface
πΈπππ map not relevant for diffusion paths because H motion in x and y directions necessary to characterize transition
Analysis of diffusion process on surface with Temperature accelerated MD
(TAD, low T=500K, high T=1300K) used to calculated πΈ(π)β(π)
show (fig.2):
Hydrogen adsorption and diffusion on W surface 2/3
(T) (T2)
additional ads. site (T2) with πΈπππ = 2.15ππ (fig.1)
transition π β π΅ : πΈ π β(π΅) β 0.55ππ
transition π΅ β π : πΈ π΅ β(π) β 0.35ππ
πΈ(π)β(π) < 0.35ππ for other transitions
transitions between adjacent ads. sites
H migration between lattice cells
through (B) sites.
Transition analysis suggests that H diffusion on
surface limited by transition π β π΅ and thus activation energy for diffusion πΈπ· β πΈ(π)β(π΅) β
0.55ππ. BUTβ¦ (see next slide)
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Act.energy for transitions btw adsorption sites
W surface πΈπ [ππ]
Figure 2
Figure 1
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BUTβ¦ πΈ π β π ,πβ (π΅) < πΈ(π)β(π΅) β H explores (T,T2,O,D) before exploring (B)
H easily migrates from (T) to (D) πΈ π β π· < 0.1eV , which tends to modify effective
potential structure in lattice cells and affect migration to other lattice cells:
During TAD run, H resides in (T,T2,D,0) much longer
than in (B) π‘πππ (π,π2,π·,0)
~10β7π >> π‘πππ (π΅)~10β9π
H diffusion on W surface might be complex:
pre-exponential factor and πΈπ· in H diffusion coefficient
may depend on temperature
Experimental measurements of H diffusion coefficient on W surface for
T>220K [Daniels1995] show πΈπ· β 0.30ππ:
in reasonable agreement with πΈπ ππ‘πβ(π) β 0.35ππ πππ πΈ(π)β π΅ β 0.55ππ
πΈπ· < πΈ(π)β π΅ in agreement with assumption of complex H diffusion
Conclusions:
W-H interatomic potential may well describe main features of adsorption sites on W
surfaces
Existence of many ads. sites may induce complex H diffusion on W surfaces
Better assessment of W-H interatomic potential required (DFT?) for further
quantitative analysis of adsorption and diffusion of H on W surfaces. For instance,
existence of (D) sites is questionable regarding their narrowness.
Hydrogen adsorption and diffusion on W surface 3/3
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H molecular desorption = H recombination into π»2 + desorption of π»2 from surface
π»2 dissociation experimentally observed on tungsten surface [Hickmott1960]
β H recombination into π»2 governs hydrogen molecular desorption
MD simulations of H molecular desorption on W surface:
Characteristic time of desorption process: ππππ ~ 1013πβπΈπππ π
β1
π
Experimental H molecular desorption activation energy πΈπππ β 1.6ππ [Tamm1971]
High simulation temperatures required: for T 1ππ
TAD simulations cannot be used because dramatic decrease of TAD efficiency with more
than one H
At T>2000K, H diffuse from W surface into W bulk
βΉ dramatic decrease of H surface coverage π and of recombination rate of H into π»2
Injection of H at constant rate into bottom layers of W samples (fig. 3) to balance H
desorption + maintain π > 0.1 + steady desorption to estimate desorption rates
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Hydrogen molecular desorption from W surface 1/3
H
π»2
tungsten
π»
Figure 3
Time [10xps]
# d
eso
rbe
d a
tom
s
Figure 4
At T=2500K (fig. 4):
Desorption of H as single atom
NO π»2 desorption for π‘π ππ β 5ππ β« ππππ
MD results contradict experimental
observations!
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To determine why no H molecular desorption at T=2500K:
Calculation of potential energy πΈπ of 2 H atoms on frozen W
surface moving toward each other along the same axis in the
plan of W surface layer (z=0) to force H recombination (fig.
5+6)
Large and sharp H recombination barrier (~ 7eV)
when H-H distance is about 1.6β« (red curve on fig 6)
Hydrogen molecular desorption from W surface 2/3
Figure 5
When all three-body interactions (TBI) involving H in
Tersoff potential turned off (TBI amplitude πΎ = 0): no more large H recombination barrier (brown curve
on fig. 6)
In [Juslin2005], amplitude of H-W-H interactions
πΎπ»βπβπ» = 12.33 much larger than other TBI involving 2H (πΎ < 0.1)
Ξ³=0
ππππ‘ = ππ πππ ππ πππ +1
1 + ππ πππ πΎππππ ππππ ππ3 πππβπππ
πβ π,π
ππ΄ ππππβ ππ
Magnitude of TBI Tersoff potential
Sharp recombination barrier β when πΎπ»βπβπ» β (fig.6)
activation energy π¬π for H recombination into π―π on W surface may strongly depends on πΈπ―βπΎβπ―
Figure 6
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activation energy πΈπ for H recombination into π»2 may strongly depend on πΎπ»βπβπ» => validation with MD simulations at 2500K (fig. 7+8):
π»2 desorption rate increases when πΎπ»βπβπ» β
when Ξ³HWH > 1, desorption rate very low due to high value of πΈπ > 2ππ
when Ξ³HWH = 0, π»2 sticked to W surface, which may contradict π»2 dissociation on W surface experimentally observed [Hickmott1960]
0 < πΎπ»βπβπ» < 1 to qualitatively reproduce H molecular desorption from W
MD simulations for πΎπ»βπβπ»= 0.55 and different temperatures: Arrhenius plot(fig. 9) gives πΈdes β πΈπ β 1.5ππ in agreement with exp. values πΈdes β 1.6ππ[Tamm1971]
Conclusions:
W-H potential in [Juslin2005] dot not qualitatively describe H recombination into π»2 because TBI parameters
πΈπ―βπΎβπ― ~π. π needed when H molecular recombination expected in MD
Hydrogen molecular desorption from W surface 3/3
Figure 9
ππππ = π. ππ ππππ = π. ππ
Figure 7 Figure 8
Time [ps]
# d
eso
rbe
d a
tom
s
Time [ps]
# d
eso
rbe
d a
tom
s
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Investigations on effects of high hydrogen surface concentration on hydrogen
recombination process suggested by experimental data (fig. (b,c) [Alnot1989])
MD simulations performed for H coverage π~0.1 on tungsten and surfaces at T=1500K (H atoms do not diffuse from W surface to W bulk)
After ~10ps, stable elongated hydrogen clusters on W surfaces (fig. 10)
Due to H-H distance >1.3β« in clusters, weak H-H interactions in clusters ( 3)
πΈπππ» < 0.1ππ for small clusters (π β€ 3)
Previously, πΈπππ β 2.4ππ (slide 6) so increase of binding energy of H to W surface
in large clusters: ΞEπ =πΈπππ» β πΈπππ β 0.7ππ. ΞEπ weakly varies with cluster size
Hydrogen clustering on tungsten surface 1/4
t=1ns t=10ps t=0ps
Figure 10
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ΞEπ due to sub-surface trapping sites (fig. 11), which can be reached by H atoms surrounded by other H
Sub-surface trapping sites induce stronger binding of H atoms to W surface due to
the presence of rows of W atoms above H atoms (fig. 11)
T=1500K β ππππ β 107π β1: Effects of H clustering on
H desorption cannot be observed in MD simulations
H clustering may affect hydrogen desorption by:
increasing the residency time of H in the vicinity of other H atoms
reducing qqty of isolated H which can recombine in small clusters(π β€ 3)
affecting recombination path for two adjacent H atoms in clusters
Formation and dissolution of k-atoms clusters at concentration ππ can be modeled as trapping & detrapping processes defined by:
the trapping rate ππ‘π π = ππ‘π,0π π πβπΈπ‘π(π)
π , the detrapping rate πππ‘ π = πππ‘,0π π πβπΈππ‘ π
π
the desorption rate ππππ π = ππππ ,0π π πβπΈπππ (π)
π where π π ~π (elongated cluster)
Since ΞπΈπ weakly varies with the size of large clusters:
πΈπππ π β πΈπππ + ΞπΈπππ where πΈπππ =activation energy for recomb. of two isolated H
πΈππ‘ π β πΈπ· + ΞπΈππ‘ where ΞπΈππ‘ = binding energy of hydrogen atom to cluster
By definition, ΞπΈπππ =0 for small clusters and for large clusters: ΞπΈπππ > 0 or ΞπΈπππ < 0
Hydrogen clustering on tungsten surface 2/4
Figure 11
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NEB: ΞπΈππ‘ β² ΞπΈπ = 0.7ππ for large clusters and ΞπΈππ‘ < 0.1ππ for small clusters
Exp. values of πΈπππ :πΈπππ β 1.6ππ [Tamm1971] β ππππ βͺ πππ‘ (fast detrapping)
When :
total H surface concentration ππ‘ππ‘ small enough to avoid cluster percolation: πΏπ π ππ‘ππ‘ βͺ 1 where πΏπ(π) = typical length of k-atoms clusters
fast diffusion compared to cluster dissolution (ππ‘ππ‘π·π» β« πππ‘)
No significant activation energy for trapping of H in clusters (πΈπ‘π < πΈππ‘)
Then cluster formation limited by diffusion of H atoms (πΈπ‘π(π) β πΈπ·)
H clusters not diffusing on surface
Within previous assumptions:
equilibrium of cluster surface concentrations ππ is determined by the balance between formation and dissolution of clusters
coexistence of large and small clusters is only possible in a very narrow range of
temperature and hydrogen concentration
Surface coverage regime determined by the nucleation process of small clusters:
if fast nucleation ππππ’π π‘ππ =ππ‘π 2,3 π
πππ‘ 2,3> 1 , large clusters dominate (large cluster regime LCR)
if slow nucleation (ππππ’π π‘ππ < 1), small clusters dominate (small cluster regime SCR)
ΞπΈππ‘ < 0.1ππ for small clusters, ππππ’π π‘ππ β πΆ0π with πΆ0~π 1 (LCR when π > 0.1)
Hydrogen clustering on tungsten surface 3/4
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Effects of H clustering on H desorption estimated with ratio R:
π = ππ‘π πβ1 ππβ1 π1ππππ π πππππ‘ π ππ
desorption from kβatom cluster
/ππ‘π 2 π1
2ππππ 2 π2
πππ‘ 2 π2
desorption from 2βatoms clusters
β π β πΆπ πππβ1
π1 πβ
ΞπΈπππ βΞπΈππ‘π , πΆπ ~π(1) (2)
Time evolution of ππ‘ππ‘ is then described by (3) where Ξπππ is the desorption flux
πππ‘ππ‘ππ‘= Ξπππ β 2ππππ ,0π
βπΈπππ π π12 1 + πΆπ ππππ₯
πππππ₯π1πβΞπΈπππ βΞπΈππ‘π
π
, πΆπ ~π(1) (3)
In LCR (ππππ’π π‘ππ > 1), ππ‘ππ‘ β ππππ₯πππππ₯ with πππππ₯ β« ππ and πππππ₯ ~π1π with π~ππππ₯:
if π β« 1, cluster-controlled desorption regime: H desorption dominated by recombination in large clusters and ππ ππ β π½πππ. Effective desorption energy π¬π ππ = π¬π ππ + π«π¬π ππ β π«π¬π π and effective pre-exp. factor ππ ππ,π~ππ ππ,ππ½π/π½πππ
If π βͺ 1, hydrogen desorption is dominated by recombination in small clusters and in SCR: ππ ππβ π½πππ
π
Experiments show πΈπππ β from 1.6ππ π‘π 1ππ and ππππ ,0 β by 8 orders when
ππ‘ππ‘ > 0.5 [Alnot1989], which may be described with cluster model:
transition from SCR to LCR is sudden, at π > 0.1 and in LCR πππππ₯π1β« 1 β π >> 1
If in LCR : ΞπΈπππ β ΞπΈππ‘ β β0.6ππ β ΞπΈπππ β 0.1eV (weak effects of clustering on desorption)
If in LCR : ππππ ~ππππ ,0π1
ππ‘ππ‘βͺ ππππ ,0 β qualitative description of ππππ ,0 drop when ππ‘ππ‘ > 0.5
Hydrogen clustering on tungsten surface 4/4
ππ =ππ
ππ ππ‘π’πππ‘πππ = surface coverage of k-atoms clusters
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MD simulations performed with W-H Tersoff interatomic potential from [Juslin2005]
H adsorption and diffusion on W surface:
Many H ads. sites on W surfaces and main features of bridge sites and H migration
between ads. sites are in qualitative agreement with experimental observations.
Many adsorption sites may lead to complex H diffusion on W surface. But
quantitative analysis strongly depends on interatomic potential.
Hydrogen molecular desorption from W surface
H molecular desorption not well described by W-H Tersoff interatomic potential
Three-body interactions parameters of this potential should be adjusted to
qualitatively reproduce main features of H recombination into π»2.
Hydrogen clustering on tungsten surface
When H surface coverage is high, H clustering is observed on W surface
Kinetic model to qualitatively describe effects of clustering on molecular desorption:
large clusters regime where surface coverage is dominated by large H clusters. In
this regime, sudden variations of desorption parameters when H surface coverage
increases are qualitatively described by the model
kinetic of H desorption from W surface may be not second-order.
Quantitative descriptions of adsorption, diffusion and clustering of H on W surface
however strongly depend on W-H interatomic potential, and better assessment of
W-H potential for W-H interactions on W surface is thus required, e.g. with DFT.
Summary